Problem: $\dfrac{d}{dx}[x^6]=$
Answer: $x^6$ is of the form $x^n$ and therefore we can apply the power rule: $\dfrac{d}{dx}[x^n]=n\cdot x^{n-1}$ $\begin{aligned} \dfrac{d}{dx}[x^{{6}}]&={6}x^{{6}-1} \\\\ &=6x^5 \end{aligned}$ In conclusion, $\dfrac{d}{dx}[x^6]=6x^5$